A pendulum is released so that its first swing covers a distance of 50\,cm. Because of air resistance, each successive swing covers 80\% of the distance of the previous swing.
a. (i) Write the distance (in cm) covered on the first, second, and third swings.
b. (ii) Derive an expression for the total distance Dn travelled in the first n swings.
c. (iii) Using your expression from part (ii), find the total distance travelled in the first 12 swings. Give your answer correct to two decimal places.